Time-Dependent Spectral Analysis of Nonstationary Time Series
非平稳时间序列的时变谱分析AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接研究非平稳时间序列的时变频谱，并明确允许突变及自适应分段。
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非平稳时间序列的时变谱分析
- 研究问题
- 如何同时描述非平稳时间序列频谱的突变与平滑变化，并根据变化速度自适应划分近似平稳的分析区间？
- 方法与思路
- 作者引入分段局部平稳过程类，采用二叉树和加窗谱进行非参数自适应分段，再估计随时间变化的频谱。
- 材料陈述的贡献
- 摘要称该过程类可近似表现为分段平稳，模拟显示分段方法能适应谱变化速度，并应用于语音和地震数据。
- 阅读关注点
- 应核对局部平稳的定义、突变与平滑变化的条件，以及分段准则、窗口选择和时变谱估计的理论保证。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；分段误差、谱估计收敛性质和模拟比较细节未说明，不能推断刊本变化。
原文摘要
Modeling of nonstationary stochastic time series has found wide applications in speech processing, biomedical signal processing, seismology, and failure detection. Data from these fields have often been modeled as piecewise stationary processes with abrupt changes, and their time-varying spectral features have been studied with the help of spectrograms. A general class of piecewise locally stationary processes is introduced here that allows both abrupt and smooth changes in the spectral characteristics of the nonstationary time series. It is shown that this class of processes behave as approximately piecewise stationary processes and can be used to model various naturally occuring phenomena. An adaptive segmentation method of estimating the time-dependent spectrum is proposed for this class of processes. The segmentation procedure uses binary trees and windowed spectra to nonparametrically and adaptively partition the data into approximately stationary intervals. Results of simulation studies demonstrate that the method has excellent ability to adapt to the rate at which the spectrum is changing. Applications of the method to speech signals and earthquake data are considered.